Wave Unit Practice Questions
If the speed of sound in air is 340 m/s the length of the organ pipe, open at both ends, that can resonate at the fundamental frequency of 136 Hz, would be: A) 0.40 m B) 0.80 m C) 1.25 m D) 2.5 m
C) For an open-open pipe the harmonic frequency is given by. L nv f n 2 with n=1
Rarefactions
The reduction of an item's density, the opposite of compression; the area of low relative pressure in a longitudinal wave
Mode Number
A normal mode is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation; helps to quantify the number of possible waves
Compressions
A region in a longitudinal wave where the particles are closest together; the region of higher pressure in a longitudinal wave
Sonic Boom
A shock wave that is produced by an aircraft or other flying object at a speed equal to or exceeding the speed of sound and that is heard on the ground as a sound similar to the loud clap of thunder
Medium
A substance that makes possible the transfer of energy from one location to another, especially through waves; the medium as a whole does not travel
Longitudinal Wave
A wave in which the particles in the medium move parallel to the direction in which the wave travels
Transverse Wave
A wave in which the particles in the medium move perpendicular to the direction in which the wave travels
The figure above shows a transverse wave traveling to the right at a particular instant of time. The period of the wave is 0.2 seconds. What is the amplitude of the wave? A) 4 cm B) 5 cm C) 8 cm D) 10 cm
A) By inspection
Assume that waves are propagating in a uniform medium. If the frequency of the wave source doubles then: A) The wavelength of the wave halves B) The wavelength of the wave doubles C) The speed of the wave halves D) The speed of the wave doubles
A) For a given medium, speed is constant. Doubling the frequency halves the wavelength
If the frequency of the sound wave is doubled, the wavelength: A) Halves and the speed remains unchanged B) Doubles and the speed remains unchanged C) Halves and the speed halves D) Doubles and the speed doubles
A) Frequency and wavelength are inverses
A person vibrates the end of a string sending transverse waves down the string. if the person then doubles the rate at which he vibrates the string while maintaining the same tension, the speed of the waves: A) Is unchanged while the wavelength is halved B) Is unchanged while the wavelength is doubled C) Doubles while the wavelength doubled D) Doubles while wavelength is halved
A) Since the medium stays the same the speed remains constant. Based on v = f λ, for constant speed, f and λ change as inverses.
A vibrating tuning fork sends sound waves into the air surrounding it. During the time in which the tuning fork makes one complete vibration, the emitted wave travels: A) One wavelength B) About 340 meters C) A distance directly proportional to the square root of the air density D) A distance inversely proportional to the square root of the pressure
A) The time to make 1 cycle, is also the time it takes one wave to travel one wavelength
The figure above shows two wave pulses that are approaching each other. Which of the following best shows the shape of the resultant pulse when the centers of the pulses, points P and Q, coincide? P is one box traveling to the right and Q is a half box on top and half box on bottom traveling to left. A) Large box to left B) Large and small box in the center C) Large box in the center D) Large box on top and a small box on the bottom in the center
A) Use superposition and overlap the waves to see the resultant
A string is firmly attached at both ends. When a frequency of 60 Hz is applied, the string vibrates in the standing wave pattern shown. Assume the tension in the string and its mass per unit length do not change. Which of the following frequencies could NOT also produce a standing wave pattern in the string? A) 30 Hz B) 40 Hz C) 80 Hz D) 180 Hz
A) The given diagram is the 3rd harmonic at 60 Hz. That means the fundamental is 20Hz. The other possible standing waves should be multiples of 20
Multiple correct: A standing wave pattern is created on a guitar as a person tunes the guitar by changing the tension in the string. Which of the following properties of the waves on the string will change as a result of adjusting only the tension in the string? Select two answers: A) The speed of the traveling wave that creates the pattern B) The wavelength of the standing wave C) The frequency of the standing wave D) The amplitude of the standing wave
A, C) Based on l m F v t , the tension changes the speed. Then based on L nv f n 2 , this resulting speed change will effect the frequency also. But since the frequency increases in direct proportion to the speed, and v = f λ, the λ should remain unchanged. Note: equation of wave speed not required
Multiple Correct: Two fire trucks have sirens that emit waves of the same frequency. As the fire trucks approach a person, the person hears a higher frequency from truck X than from truck Y. Which of the following statements about truck X can be correctly inferred from this information? Select two answers: A) It is traveling faster than truck Y B) It is closer to the person than truck Y C) It is speeding up and truck Y is slowing down D) Its wavefronts are closer together than truck Y
A, D) Based on the Doppler effect, only speed matters. The faster a vehicle is moving, the closer together the sound waves get compressed and the higher the frequency. Take the case of a very fast vehicle traveling at the speed of sound; the compressions are all right on top of each other. So faster speed means closer compressions and higher frequencies. Choice I must be true because X is a higher frequency so must be going faster. Distance to the person affects the volume but not the pitch so choice II is wrong. III seems correct but its not. It doesn't matter whether you are speeding up or slowing down, it only matters who is going faster. For example, suppose truck X was going 5 mph and speeding up while truck Y was going 50 mph and slowing down, this is an example of choice III but would not meet the requirement that X has a higher frequency because only actual speed matters, not what is happening to that speed.
Assume the speed of sound is 340 m/s. One stereo loudspeaker produces a sound with a wavelength of 0.68 meters while the other speaker produces sound with a wavelength of 0.65 m. What would be the resulting beat frequency? A) 3 Hz B) 23 Hz C) 511.5 Hz D) 11,333 Hz
B) Determine each separate frequency using the speed of sound as 340 and v = f λ. Then subtract the two frequencies to get the beat frequency
Two wave pulses approach each other as seen in the figure. The wave pulses overlap at point P. Which diagram best represents the appearance of the wave pulses as they leave point P? The figure includes a box traveling from the left to the right and an upside down triangle traveling from the right to the left with point P in the middle. A) Box traveling to the left and triangle traveling to the right B) Triangle traveling to left and box traveling to the right C) Cone traveling to the right D) Cone traveling to the left
B) After waves interfere they move along as if they never met
A small vibrating object S moves across the surface of a ripple tank producing the wavefronts as shown above. The wavefronts move with speed v. The object is traveling in what direction and with what speed relative to the speed of the wavefronts produced? DIRECTION SPEED A) To the right Equal to v B) To the right Less than v C) To the left Less than v D) To the left Greater than v
B) Doppler effect. The waves at right are compressed because the object is moving right. However, the waves are moving faster than the object since they are out in front of where the object is.
The frequencies of the first two overtones (second and third harmonics) of a vibrating string are f and 3f/2. What is the fundamental frequency of this string? A) f/3 B) f/2 C) f D) 2f
B) Harmonics are multiples of the fundamental so the fundamental must be f/2
Two wave pulses, each of wavelength omega, are traveling toward each other along a rope as shown. When both pulses are in the region between points X and Y which are a distance omega apart, the shape of the rope is: A) Bump to right B) Straight Line C) Sinusoidal D) Bump to bottom right
B) Superpose the two waves on top of each other to get the answer
A standing wave of frequency 5 Hz is set up on a string 2 meters long with nodes at both ends and in the center, as shown above. There are two antinodes and three nodes. The fundamental frequency of vibration of the string is: A) 1 Hz B) 2.5 Hz C) 5 Hz D) 10 Hz
B) The diagram shows the second harmonic in the string. Since harmonics are multiples, the first harmonic would be half of this.
The graph below was produced by a microphone in front of a tuning fork. It shows the voltage produced by the microphone as a function of time. In order to calculate the speed of sound from the graph, you would also need to know A) Pitch B) Wavelength C) Frequency D) Volume
B) To use v = f λ, you also need the λ
As sound travels from steel into the air both its speed and its: A) Wavelength increase B) Wavelength decrease C) Frequency increase D) Frequency remain unchanged
B) When sound travels into less dense medium, its speed decreases (unlike light) ... however, like all waves when traveling between two mediums, the frequency remains constant. Based on v = f λ, if the speed decreases and the frequency is constant then the λ must decrease also.
Multiple correct: In the Doppler Effect for sound waves, factors that affect the frequency that the observer hears include which of the following? Select two answers: A) The loudness of the sound B) The speed of the source C) The speed of the observer D) The phase angle
B, C) A fact about the Doppler effect. Can also be seen from the Doppler equation (which is not required).
Multiple Correct: The diagrams above represent 5 different standing sound waves set up inside of a set of organ pipes 1 meter long. Which of the following statements correctly relates the frequencies of the organ pipes shown? Select two answers: A) Cy is twice the frequency of Cx B) Cz is five times the frequency of Cx C) Oy is twice the frequency of Ox D) Ox is twice the frequency of Cx
B, C) Wavelengths of each are (dist/cycle) ... 4L, 4/3 L, 4/5 L, L, 2/3 L ... Frequencies are f = v/ λ. v/4L, 3v/4L, 5v/4L, v/L, 3v/2L ... Oy is 2x Cy
The figure above shows a transverse wave traveling to the right at a particular instant of time. The period of the wave is 0.2 seconds. What is the speed of the wave? A) 4 cm/s B) 25 cm/s C) 50 cm/s D) 100 cm/s
C) By inspection, the λ is 10 cm. f = 1 / T = 5, Then use v = f λ.
A small vibrating object on the surface of a ripple tank is the source of waves of frequency 20 Hz and speed 60 cm/s. If the source S is moving to the right as shown, with speed 20 cm/s, at which of the labeled points will the frequency measured by a stationary observer be greatest? A) A B) B C) C D) D
C) Clearly at point C the waves are compressed so are more frequent
The diagram shows two transverse pulses moving along a string. One pulse is moving to the right and the second is moving to the left. Both pulses reach point x at the same instant. What would be the resulting motion of point x as the two pulses pass each other? A) down, up, down B) up then down C) up, down, up D) There would be no motion, the pulses cancel one another
C) Step the two pulses through each other a little bit at a time and use superposition to see how the amplitudes add. At first the amplitude jumps up rapidly, then the amplitude moves down as the rightmost negative pulse continues to propagate. At the very end of their passing the amplitude would be all the wave down and then once they pass the point will jump back up to equilibrium
What would be the wavelength of the fundamental and first two overtones produced by an organ pipe of length L that is closed at one end and open at the other? A) L, 1/2L, 1/4L B) 1/2L, 1/4L, 1/6L C) 4L, 4/3L, 4/5L D) 4L, 2L, L
C) This is similar to question 26, except now the length of the tube remains constant and the wave is changing within the tube to make each successive waveform (this would be like using different tuning forks each time for the same tube). The diagrams would look like this now: 5 3 1 Each λ is given by λ = dist / cycle So λ1 = 4L λ3 = 4/3 L λ5 = 4/5 L
A tube is open at both ends with the air oscillating in the fourth harmonic. How many displacements nodes are located within the tube? A) 2 B) 3 C) 4 D) 5
C) To produce pipe harmonics, the ends are always antinodes. The first (fundamental) harmonic is when there are two antinodes on the end and one node in-between. To move to each next harmonic, add another node in the middle and fill in the necessary antinodes. (ex, 2nd harmonic is ANANA ... So the 4th harmonic would be ANANANANA and have four nodes. Alternative solution ... if you know what the harmonics look like you can draw them and manually count the nodes
Multiple correct: One end of a horizontal string is fixed to a wall. A transverse wave pulse is generated at the other end, moves toward the wall as shown and are reflected at the wall. Properties of the reflected pulse include which of the following. Select two answers: A) It has a greater speed than that of the incident pulse B) It has a greater amplitude than that of the incident pulse C) It is on the opposite side of the string from the incident pulse D) It has a smaller amplitude than that of the incident pulse
C, D) When hitting a fixed boundary, some of the wave is absorbed, some is reflected inverted. The reflected wave has less amplitude since some of the wave is absorbed, but since the string has not changed its properties the speed of the wave should remain unchanged.
A standing wave of frequency 5 Hz is set up on a string 2 meters long with nodes at both ends and in the center, as shown above. There are two antinodes and three nodes. The speed at which waves propagate on the string is: A) 0.4 m/s B) 2.5 m/s C) 5 m/s D) 10 m/s
D) Based on the diagram, the wavelength is clearly 2 meters and plug into v = f λ.
The standing wave pattern diagrammed to the right is produced in a string fixed at both ends. The speed of waves in the string is 2 m/s. What is the frequency of the standing wave pattern? A) 0.25 Hz B) 1 Hz C) 2 Hz D) 4 Hz
D) From diagram, wavelength = 0.5 m Find frequency with v = f λ
A pipe that is closed at one end and open at the other resonates at the fundamental frequency of 240 Hz. The next lowest/highest frequency it resonates at is most nearly: A) 80 Hz B) 120 Hz C) 480 Hz D) 720 Hz
D) Open-closed pipes only have odd multiple of harmonic, so next is 3x(f1)
For a standing wave mode on a string fixed at both ends, adjacent antinodes are separated by a distance of 20 cm. Waves travel on this string at a speed of 1200 cm/s. At what frequency is the string vibrated to produce this standing wave? A) 120 Hz B) 60 Hz C) 40 Hz D) 30 Hz
D) Two antinodes by definition will be ½ λ apart. So 20 cm = ½ λ, and the λ = 40 cm. Then using v = f λ we have 1200 = f (40)
A tube of length L1 is open at both ends. The second tube of length L2 is closed at one end and open at the other end. This second tube resonates at the same fundamental frequency as the first tube. What is the value of L2? A) 4L1 B) 2L1 C) L1 D)1/2 L1
D) We should look at the harmonic shapes open-open vs open-closed. L1 L2 Comparing the fundamental harmonic of the open-open pipe to the closed-open pipe. The closed-open pipe should be half as long as the open-open pipe in order to fit the proper number of wavelengths of the same waveform to produce the given harmonic in each.
The graph below was produced by a microphone in front of a tuning fork. It shows the voltage produced by the microphone as a function of time. The frequency of the tuning fork is approximately: A) 0.004s B) 0.020s C) 50 Hz D) 250 Hz
D) f = cycles/second
Antinodes
Points halfway between the nodes where the particles oscillate in the medium with maximum displacement; these points are also spaced one half of a wavelength apart; the wavelength of a standing wave is twice the distance between successive nodes or antinodes
Doppler Effect
The change of frequency when a source moves relative to an observer
Standing Wave
The crests and troughs of the wave "standing in place" as the wave oscillates; the wave itself doesn't travel left or right; it is typically between two boundaries/ends
Wavelength
The distance spanned by one cycle of motion of a given wave
Amplitude
The maximum value of displacement of the particles on a wave
Fundamental Frequency
The most fundamental harmonic associated with a standing wave having only one antinode positioned between the two nodes at the end of the string; the harmonic of the lowest wavelength and the lowest frequency
Nodes
The points on a standing wave that never move, which are equally spaced half of a wavelength apart
Harmonics
The sequence of possible frequencies and the frequencies above the fundamental frequency are "higher harmonics"
Electromagnetic Waves
Waves of an electromagnetic field; very diverse, including visible light, radio waves, microwaves, and x-rays; require no material medium to travel through
Mechanical Wave
Waves that involve the motion of a substance through which they move, the medium
Constructive Interference
When the displacements of two waves are both positive, so the total displacement of the medium where they overlap is larger than it would be due to either of the waves separately
Principle of Superposition
When two or more waves are simultaneously present at a single point in space, the displacement of the medium at the point is the sum of the displacements due to each individual wave
Beats
When two sound waves of different frequency approach your ear, the alternating constructive and destructive interference cause the sound to alternate soft and loud
Destructive Interference
Where the displacement of a medium after an interference is less than it would be due to either of the waves traveling separately